#include <bits/stdc++.h>
#define pii pair<long long, int>
using namespace std;
int N, M;
int S, T, U, V;
vector<pii> adj[100005];
vector<int> child[100005];
long long best[2][100005];//0 -> S, 1 -> T
long long dist[2][100005];//0 -> U, 1 -> V
long long dp[2][100005];
priority_queue<pii, vector<pii>, greater<pii>> pq;
long long opt, ans = 4e18;
void find_opt(int init, int id) {
pq.emplace(0, init);
best[id][init] = 0;
int u, v;
long long len, w;
while(!pq.empty()) {
u = pq.top().second;
len = pq.top().first;
pq.pop();
for(pii now : adj[u]) {
v = now.second;
w = now.first;
if(best[id][v] > len + w) {
best[id][v] = len + w;
pq.emplace(best[id][v], v);
}
}
}
}
void make_DAG() {
opt = best[0][T];
int u, v;
long long w;
for(u = 1; u <= N; u++) {
for(pii now : adj[u]) {
v = now.second;
w = now.first;
if(best[0][u] + w + best[1][v] <= opt) child[u].emplace_back(v);
}
}
}
void find_dist(int init, int id) {
pq.emplace(0, init);
dist[id][init] = 0;
int u, v;
long long len, w;
while(!pq.empty()) {
u = pq.top().second;
len = pq.top().first;
pq.pop();
for(pii now : adj[u]) {
v = now.second;
w = now.first;
if(dist[id][v] > len + w) {
dist[id][v] = len + w;
pq.emplace(dist[id][v], v);
}
}
}
}
long long depe(int id, int u) {
if(u == T) return dist[id][T];
if(dp[id][u] != -1) return dp[id][u];
long long res = dist[id][u];
for(int v : child[u]) {
res = min(res, depe(id, v));
}
return dp[id][u] = res;
}
void solve() {
find_opt(S, 0);
find_opt(T, 1);
make_DAG();
find_dist(U, 0);
find_dist(V, 1);
ans = dist[0][V];
for(int i = 1; i <= N; i++) {
if(child[i].size() == 0) continue;
ans = min(ans, dist[0][i] + depe(1, i));
ans = min(ans, dist[1][i] + depe(0, i));
}
printf("%lld\n", ans);
cin >> N;
}
int main() {
memset(dp, -1, sizeof(dp));
memset(best, 0x3f3f3f3f, sizeof(best));
memset(dist, 0x3f3f3f3f, sizeof(dist));
scanf("%d %d %d %d %d %d", &N, &M, &S, &T, &U, &V);
int u, v, w;
for(int i = 1; i <= M; i++) {
scanf("%d %d %d", &u, &v, &w);
adj[u].emplace_back(w, v);
adj[v].emplace_back(w, u);
}
solve();
}
